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Fundamentalnaya i Prikladnaya Matematika, 2006, Volume 12, Issue 8, Pages 29–77
(Mi fpm28)
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This article is cited in 10 scientific papers (total in 10 papers)
Elementary equivalence of Chevalley groups over fields
E. I. Bunina M. V. Lomonosov Moscow State University
Abstract:
It is proved that (elementary) Chevalley groups $G_\pi(\Phi,K)$ and $G_{\pi'}(\Phi',K')$
(or $E_\pi (\Phi,K)$ and $E_{\pi'}(\Phi',K')$) over infinite fields $K$ and $K'$ of characteristic different from 2, with weight lattices $\Lambda$ and $\Lambda'$, respectively, are elementarily equivalent if and only if the root systems $\Phi$ and $\Phi'$ are isomorphic, the fields $K$ and $K'$ are elementarily equivalent, and the lattices $\Lambda$ and $\Lambda'$ coincide.
Citation:
E. I. Bunina, “Elementary equivalence of Chevalley groups over fields”, Fundam. Prikl. Mat., 12:8 (2006), 29–77; J. Math. Sci., 152:2 (2008), 155–190
Linking options:
https://www.mathnet.ru/eng/fpm28 https://www.mathnet.ru/eng/fpm/v12/i8/p29
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